Using a REST API can be as simple as opening an URL in your browser. More examples on that here: http://lithosphere.lithium.com/t5/Support-Knowledge-Base/Working-with-Rest-API-search/ta-p/39942
Restful APIs are a general concept and there are some examples explaining the concept and working with them on the web, e.g. here: http://www.peej.co.uk/articles/restfully-delicious.html
Feel free to share a more specific Lithium REST API question once you've played around a bit.